论文标题
Josefson - 本地凸空间的Nissenzweig属性
The Josefson--Nissenzweig property for locally convex spaces
论文作者
论文摘要
如果身份映射映射$（e'，σ（e'，e））\ to（e'，β^\ ast（e'，e））$，我们不是连续持续的。根据经典的Josefson-Nissenzweig定理，每个无限的Banach空间都有JNP。给出了用JNP局部凸出空间的表征。我们在各种功能空间中彻底研究JNP。除其他结果外，我们还表明，对于Tychonoff空间$ x $，功能空间$ C_P（X）$具有JNP IFF，$^\ ast $ null-sequence $（μ_n）_ {n \inΩ} $的$ x $具有单位标准的$ x $。但是，对于每一个Tychonoff空间$ x $，$ x $上的baire-1 $ b_1（x）$都不是$ x $上的免费本地凸出空间$ l（x）$ ax $ x $的jnp。
We define a locally convex space $E$ to have the $Josefson$-$Nissenzweig$ $property$ (JNP) if the identity map $(E',σ(E',E))\to ( E',β^\ast(E',E))$ is not sequentially continuous. By the classical Josefson-Nissenzweig theorem, every infinite-dimensional Banach space has the JNP. A characterization of locally convex spaces with the JNP is given. We thoroughly study the JNP in various function spaces. Among other results we show that for a Tychonoff space $X$, the function space $C_p(X)$ has the JNP iff there is a weak$^\ast$ null-sequence $(μ_n)_{n\inω}$ of finitely supported sign-measures on $X$ with unit norm. However, for every Tychonoff space $X$, neither the space $B_1(X)$ of Baire-1 functions on $X$ nor the free locally convex space $L(X)$ over $X$ has the JNP.
